What if you were given
and told that
was its midsegment? How could you find the length of
given the length of the triangle's third side,
? After completing this Concept, you'll be able to use the Midsegment Theorem to solve problems like this one.

Guidance

A line segment that connects two midpoints of the sides of a triangle is called a
midsegment
.
is the midsegment between
and
.

The tic marks show that
and
are midpoints.
and
. For every triangle there are three midsegments.

There are two important properties of midsegments that combine to make the
Midsegment Theorem
. The
Midsegment Theorem
states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side. So, if
is a midsegment of
, then
and
.

Note that there are two important ideas here. One is that the midsegment is parallel to a side of the triangle. The other is that the midsegment is always half the length of this side. To play with the properties of midsegments, go to
http://www.mathopenref.com/trianglemidsegment.html
.

Example A

The vertices of
are
and
. Find the midpoints of all three sides, label them
and
Then, graph the triangle, plot the midpoints and draw the midsegments.

To solve this problem, use the midpoint formula 3 times to find all the midpoints. Recall that the midpoint formula is
.